The Serie A champions were made to work extremely hard for their 3-2 win over Olympiacos in the UEFA Champions League on Tuesday, but they were back to their ruthless best as the three strikers starred on Sunday.
Juve were 3-0 up at the break as Llorente twice knocked in simple finishes and Stephan Lichtsteiner drove a ferocious half-volley beyond the helpless Antonio Mirante.
Massimiliano Allegri had something of a defensive injury crisis to contend with pre-match, as Kwadwo Asamoah, Patrice Evra, Andrea Barzagli and Martin Caceres all missed out.
Yet Parma struggled to make any impact as an attacking force and Tevez netted twice in the first 15 minutes of the second half, first scoring an incredible solo effort and then pouncing on a rebound.
Juve still had it in them to net two more as Morata, a 71st-minute replacement for Llorente, coolly slotted home 14 minutes from time and then added the seventh at the death to mark his first Spain call-up in style.
Under-pressure Donadoni attempted to rally his men in the build-up, but Juve were utterly dominant right from the start, with Roberto Pereyra's over-head kick serving as a warning after just eight minutes.
Parma struggled to come to terms with Juve's clever use of the ball in the final third and it came as little surprise when the hosts finally took the lead in the 23rd minute.
Mirante failed to hold on to Paul Pogba's 20-yard effort and Llorente was on hand to tap in the rebound.
They doubled their lead just six minutes later and in spectacular fashion.
Lichtsteiner ran on to a loose ball 25 yards from goal and met it with an unstoppable half-volley, giving Mirante no chance in the Parma net.
The Swiss full-back was integral again as Juve opened up a three-goal lead in the 36th minute, cutting an intelligent cross behind a crowd of players in the area to set up an easy finish for Llorente.
Juventus looked determined to punish Parma at the start of the second period, despite already holding a comfortable lead.
And Tevez single-handedly scored the hosts' fourth in the 50th minute as the Argentina forward ran from well inside his own half, dribbled past two defenders and produced a tidy finish into the bottom-right corner to complete a sensational goal.
Tevez's second arrived eight minutes later as he tapped past Mirante from 10 yards after the goalkeeper could only parry a Pogba effort.
Juve added number six 14 minutes from time as Kingsley Coman, introduced for Tevez, produced an audacious chipped pass over the Parma defence and Morata prodded past Mirante.
The young Spaniard rounded off an incredible win for the hosts in the 88th minute as he steered Lichtsteiner's cross into the top-right corner with a precise volley.